From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which sho…

Question

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be in...

Accepted Answer

1 Captain, 1 vice-captain are already present

$\Rightarrow$ We need to select 8 players such that atleast 3 batsman and bowler must be there

Batsman
 Bowler
 Number of ways

3
 5
 ${}^{6}{C}_{3}\cdot {}^{5}{C}_{5}=20$

4
 4
 ${}^{6}{C}_{4}\cdot {}^{5}{C}_{4}=75$

5
 3
 ${}^{6}{C}_{5}\cdot {}^{5}{C}_{3}=60$

Total = 155 ways

Solutions · 1